Details on how to show a display in the other process monitoring tool is really best adressed for the developer of this tool, and any community there.

But you can bring in PI Vision displays using normal html iframe functionality. A tip would be to take advantage of the query string parameters available to PIVision, to control how far end-users can navigate inside the iframe.

Have a look at the section "URLs to open displays" in the LiveLibrary: PI Vision

There is a section on "Embedded displays" which'll (probably) fix your security issue. Other interesting things would be URL parameters, such as asset, mode=kiosk, hidetimebar and hidetoolbar parameters.